Some Dimensional Metrology Issues for Nanotechnology
John Villarrubia, National Institute of Standards and Technology
The Need for Nanometer-Scale Dimensional Metrology - The “nano” in
“nanotechnology” refers to the nanometer size scale. To the extent that a particular
technology is legitimately classified as a nanotechnology, it is because its function is
inextricably tied to the properties of materials at that size scale.
Having function tied to size is not new. Examples abound within existing industries. For
example, in semiconductor electronics, the capacitance of transistor gates decreases with
decreasing gate size. As a consequence of decreasing capacitance, switching speeds
increase. Therefore, other things being equal, smaller gates make faster microprocessors.
For computers, faster is better, so there is a link between the smallness of the product and
its economic value.1 Consequently, there is an incentive to push gate dimensions to the
smallest that can be reliably manufactured. However, manufacturing processes are
subject to random uncontrolled influences that cause gate sizes to fluctuate near their
target values. Because the manufacturing process is already making gates “as small as
possible,” too large of a fluctuation to the small side results in an unprintable gate—and
loss of yield. A fluctuation to the large side represents a slower transistor—and a
microprocessor that cannot be sold at the best price. Therefore, measurement of gate sizes
during production, and use of this information to control the manufacturing process,
become very important in the manufacture of this product.
It seems likely that this model, or something similar to it, will be repeated whenever size
is tied to function, as is inherently the case for the nascent nanotechnology industry.
Where component sizes are themselves measured in nanometers, a change of a few
nanometers represents a significant percentage difference, and therefore likely a
significant difference in properties. For good process control, measurement uncertainty
must be small compared to the size of these changes. With gate sizes still larger than 50
nm, the semiconductor industry already desires metrology with accuracies of 1 nm or
better.2 The requirements for trouble-shooting and process control of other
nanotechnology industries are likely to be at least as strict.
Image Artifacts and Dimensional Metrology - Dimensions of very small objects are
most commonly determined by measuring an image acquired by a microscope and
applying a correction for the scale (i.e., magnification). Images are representations of the
sample, but they are not perfect ones. Apart from the different scale, they are subject to a
number of image “artifacts.” For example, geometrical distortions may be caused by lens
imperfections or in scanning microscopies like scanning electron microscopy (SEM) or
atomic force microscopy (AFM) by scanner nonlinearities. Because of this artifact, the
scale may be different in different parts of the image, and distances that are identical on
the image may be different in the actual sample. To the extent that this kind of artifact is
consistently repeatable, it is subject to correction by calibration. An appropriate
calibration sample, for example a sample periodic at the appropriate scale or any sample
with uniquely identifiable features that can be imaged in multiple orientations, can
expose these nonlinearities and subject them to correction.
Another artifact is a consequence of a microscope’s limited spatial resolution. Point
features appear to have finite extent when imaged. Even when the image scale is
everywhere correct so objects’ center to center distances are accurately represented, their
measured widths are distorted by this effect. For larger objects, the spatial resolution is
small compared to features of interest, and this artifact is hardly noticed. For nanometerscale objects, this is no longer the case. This artifact is sometimes naively considered to
be characterized by an instrument’s point-spread function. Sometimes, there is a
component that may be correctly characterized in such a way (for instance, the effect of
the electrons’ landing spot in an SEM). However, there are important, often nonlinear,
effects that depend upon the complexities of the interaction between the microscope
“probe” (electron beam in the SEM, mechanical tip in the AFM) and the sample.
Examples of these for AFM and SEM are given in the next couple of paragraphs.
AFM images are formed by scanning the sample with a mechanical tip that is either in
contact or near-contact. This results in an image that is a dilation of the sample and tip
shapes.3 Positive features (protrusions) on the sample appear wider by an amount that
depends upon the dimensions of the tip and the heights and slopes of the tip and feature
(Fig. 1). Negative features (depressions) on the sample appear narrower by an amount
determined similarly. The details of this interaction depend upon the particular interacting
shapes. Under favorable circumstances, for example when imaging an atomically flat
surface as in early atomic-resolution scanning tunneling microscopy images, even a
relatively blunt tip can yield atomic resolution because only a very small part of it ever
interacts with the sample. More generally, however, for samples with larger slopes and
higher aspect ratio features, artifacts comparable to the size of the tip are to be expected.
This is significant because the tip is also a nanopart. Whatever fundamental limitations
determine the minimum size of manufactured parts also limit the manufacture of tips.
Hence, for nanotechnology samples, tips are likely to be of comparable size to the parts
which they must measure.
Fig. 1. The conventional model for imaging. The protrusion’s image has additional width
determined by its interaction with the tip. Figure reproduced from Reference 4.
For secondary electron imaging in the SEM, incident electrons scatter inside the sample
within some interaction volume (Fig. 2). Secondary electrons produced deep inside the
sample do not contribute to the image because they do not have enough energy to escape
the sample. Only secondary electrons generated near a surface can contribute. The
interaction volume intersects a greater part of sloped surfaces than horizontal ones,
causing such surfaces to be brighter. Whenever the interaction volume intersects a new
surface of the sample new escape routes for secondary electrons can contribute to the
image. For example, this can happen when the landing spot for the incident electron beam
approaches a corner, and secondary electrons may escape from the side as well as the top
surface. These nonlinear effects help to create the contrast pattern that defines the image.
The characteristic size of the electron volume at incident energies that are typically
employed ranges from tens to thousands of nanometers. Hence, these effects are also
important for critical nanotechnology features.
Fig. 2. Schematic showing electrons (trajectories in black) scattering inside the sample (red) and
resulting intensity dependence (blue) when the landing position is scanned. Spatial resolution is
often limited by an interaction volume larger than the beam spot size.
An Approach to Addressing the Issues - Microscopes, as discussed in the introduction,
always have image artifacts at some scale. Historically, when that scale became limiting,
better microscopies with still smaller limits were employed. The same strategy will to a
certain extent still be effective, but the nanometer scale is approaching the fundamental
limits of many kinds of interactions between probes and materials. It will consequently be
more important to understand these interactions, model them, and apply corrections. In
the AFM, if the tip shape can be measured, those parts of the sample that were probed by
the tip may be recovered from the image.3,4 In the SEM, modeling of the interaction
between the electron beam and the sample can permit location of an edge with an
accuracy better than the instrument’s resolution.5,6
These solutions have up to now been applied to samples with relatively simple shapes.
The situation is rendered more complicated in the incipient nanotechnology industries by
the geometrical complexity of some of the envisioned parts to be manufactured. Existing
models for the AFM require parts to be described as single-valued functions, f(x,y). The
existing NIST MONSEL code for SEM simulation handles only limited types of twodimensional profiles. In both cases, extending these capabilities to three-dimensional
samples will be important for nanotechnology applications.
C.P. Ausschnitt and M. E. Lagus, “Seeing the Forest for the Trees: A New Approach to CD control,”
Proc. SPIE Vol. 3332, p. 212 (1998).
2
International Technology Roadmap for Semiconductors, (Semiconductor Industry Association, 2003),
Table 117a, Metrology Section, pg. 10. (http://public.itrs.net)
3
J. S. Villarrubia, “Morphological estimation of tip geometry for scanned probe microscopy,” Surf. Sci.
321, 287 (1994).
4
J. S. Villarrubia, “Algorithms for scanned probe microscope image simulation, surface reconstruction, and
tip estimation,” J. Res. Natl. Inst. Stand. Technol. 102, 425 (1997). Also available at
http://nvl.nist.gov/pub/nistpubs/jres/102/4/j24vil.pdf.
5
J. S. Villarrubia, A. E. Vladár, J. R. Lowney, and M. T. Postek, “Scanning electron microscope analog of
scatterometry,” Proc. SPIE 4689, pp. 304-312 (2002).
6
“J. S. Villarrubia, A. E. Vladár, and M. T. Postek, A Simulation Study of Repeatability and Bias in the
CDSEM,” Proc. SPIE 5038, pp. 138-149 (2003).
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